A bakery had 15 small identical tins and 12 large identical tins. It used 1100 cookies to fill 8 small tins and 5 large tins completely. The number of cookies needed to fill 3 large tins completely was the same as the number needed to fill 4 small tins completely.
- How many cookies were needed to fill a large tin completely?
- How many more cookies were needed to fill the remaining tins completely?
Need a hint?
Write the equal-cookies link as 3 large = 4 small, then turn 8 small tins into large-tin units before adding.
Worked answer
- (a) 3 large tins = 4 small tins, so 4 small tins = 3 large tins.
- (a) Then 8 small tins = 6 large tins, so 8 small and 5 large tins = 11 large tins' worth of cookies.
- (a) 11 units of a large tin = 1100 cookies, so 1 large tin = 100 cookies.
- (a) Each small tin = 3 × 100 ÷ 4 = 75 cookies.
- (b) Remaining small tins = 15 − 8 = 7; remaining large tins = 12 − 5 = 7.
- (b) Cookies for remaining small tins = 7 × 75 = 525; for large tins = 7 × 100 = 700.
- (b) Total needed = 525 + 700 = 1225 cookies.
Answer: 1225 cookies
The mistake this question tests
Habit
Left out the units
Pupils divide 1100 by 13 tins as if all tins held the same amount, which ignores that small and large tins hold different numbers of cookies.
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